Suicide is a major public health concern accounting for 800 000 deaths globally each year. Although there have been many advances in understanding suicide risk in recent decades, our ability to predict suicide is no better now than it was 50 years ago. There are many potential explanations for this lack of progress, but the absence, until recently, of comprehensive theoretical models that predict the emergence of suicidal ideation distinct from the transition between suicidal ideation and suicide attempts/suicide is key to this lack of progress. The current article presents the integrated motivational–volitional (IMV) model of suicidal behaviour, one such theoretical model. We propose that defeat and entrapment drive the emergence of suicidal ideation and that a group of factors, entitled volitional moderators (VMs), govern the transition from suicidal ideation to suicidal behaviour. According to the IMV model, VMs include access to the means of suicide, exposure to suicidal behaviour, capability for suicide (fearlessness about death and increased physical pain tolerance), planning, impulsivity, mental imagery and past suicidal behaviour. In this article, we describe the theoretical origins of the IMV model, the key premises underpinning the model, empirical tests of the model and future research directions. This article is part of the theme issue ‘Evolutionary thanatology: impacts of the dead on the living in humans and other animals'.